a -Cluster States in Electron Scattering *

1. Darmstadt 2008 TU DARMSTADT S-DALINAC a-Cluster States in Electron Scattering * Maksym Chernykh Institut für Kernphysik, TU Darmstadt M. Chernykh1, H. Feldmeier 2, T. Neff 2, P. von Neumann-Cosel1, and A. Richter1 1Institut für Kernphysik, TU Darmstadt 2Gesellschaft für Schwerionenforschung (GSI), Darmstadt * Supported by DFG under contract SFB 634

2. Motivation: structure of the Hoyle state • Hoyle state is a prototype of a-cluster • states in light nuclei • Cannot be described by shell-model • approaches • a-cluster models predict Hoyle state • as a dilute gas of weakly interacting • a particles resembling the properties • of a Bose-Einstein Condensate (BEC) • Comparison of high-precision electron scattering data with • predictions of FMD and a-cluster models Hoyle state cannot be understood as a true Bose-Einstein Condensate ! • M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, • and A. Richter, Phys. Rev. Lett. 98 (2007) 032501

3. http://outreach.atnf.csiro.au Motivation: astrophysical importance • Triple alpha reaction rate (a,a’) (p,p’) (e,e’) (p,p’) • Reaction rate with accuracy ~ 6% needed S.M. Austin, Nucl. Phys A758 (2005) 375c

4. Motivation: astrophysical importance Crannell et al. (1967) Strehl (1970) Crannell et al. (2005) • Total uncertainty Dr3a/r3a = 11.6% only

5. Transition form factor to the Hoyle state • Fourier-Bessel analysis: Crannell (2005) • Extrapolation to zero momentum transfer: Crannell (1967), Strehl (1970) H. Crannell, data compilation

6. Model-independent extraction of the partial pair width Model-independent PWBA analysis

7. Monopole matrix element • ME = 5.37(22) fm2, Rtr = 4.24(30) fm • Large uncertainty because of narrow momentum transfer region P. Strehl, Z. Phys. 234 (1970) 416

8. Lintott spectrometer

9. 10 cm Detector system • Si microstrip detector system: • 4 modules, each 96 strips with • pitch of 650 mm • Count rate up to 100 kHz • Energy resolution 1.5x10-4

10. Measured spectra

11. Monopole matrix element

12. Triple alpha reaction rate Crannell et al. (1967) Strehl (1970) Crannell et al. (2005) Present work • Total uncertainty Dr3a/r3a = 10% • Only need to be improved

13. – – Hoyle state is important for stellar nucleosynthesis 16O: broad 0+ state at 15 MeV – – – Monopole matrix element can be extracted by extrapolation of cross section to zero momentum transfer Gp for decay of the Hoyle state with uncertainty 2.5% extracted Hoyle state: independent Fourier-Bessel analysis Summary and outlook • Outlook Thank you!

15. – – Astrophysical importance Extraction of monopole matrix element ME – Comparison with FMD and a-cluster model predictions Outline • Motivation: • Model-independent PWBA analysis • High-resolution electron scattering measurements • Results • Summary and outlook

16. Model-independent PWBA analysis • Model-independent extraction of monopole matrix element ME

17. 12C densities ↔ • Ground state density can be • tested via elastic form factor ↔ • Transition density can be tested • via transition form factor FMD : R. Roth, T. Neff, H. Hergert, and H. Feldmeier, Nucl. Phys. A745 (2004) 3 • “BEC”: Y. Funaki et al., Phys. Rev. C 67 (2003) 051306(R)

18. Elastic form factor • Described well by FMD

19. Transition form factor to the Hoyle state • H. Crannell, data compilation • Described better by a-cluster models

20. What is actual structure of the Hoyle state ? • In the “BEC” model the relative positions of a clusters should be • uncorrelated • Overlap with FMD basis states • But in the FMD and a-cluster model the leading components • of the Hoyle state are cluster-like and resemble 8Be + 4He configurations

21. – – 16O: broad 0+ state at 15 MeV Gp for decay of the Hoyle state with uncertainty 2.5% extracted + + – – – – 12C: 03 and 22 states 8Be + a structure Hoyle state: Fourier-Bessel analysis of all available data Hoyle state is not a true Bose-Einstein condensate Summary and outlook • Summary • Outlook